The theory of reliability is the new scientific disciplined that studies the general regularity that must be maintained under design, experimentation, manufacture, acceptance and use of units (components) in order to maximal effectiveness from their use.The need of obtaining highly reliable systems and components has acquired special importance with development of the present day technology.All the models have been solved by using supplementary variable technique, Laplace transformation and Gumble-Hougaard family of copula. Availabilities, asymptotic behavior, MTTF, etc. have been obtained...